The type of wave where particles in the medium vibrate in the same direction as the wave is moving is called a longitudinal wave.

Here's a breakdown:

* Longitudinal waves: The particles of the medium oscillate back and forth parallel to the direction of the wave's motion. Think of a slinky being stretched and then pushed, causing a compression and rarefaction pattern to move along the slinky. Sound waves are a great example of longitudinal waves.

* Transverse waves: The particles of the medium oscillate perpendicular to the direction of the wave's motion. Imagine a rope tied to a post and you shake it up and down. The wave travels along the rope, but the rope particles move up and down. Light waves are an example of transverse waves.